Strain regularisation using a non-local method in Coupled Eulerian-Lagrangian analyses

Conventional finite element analyses generally suffer from mesh dependency when considering softening effects. Non-local strain regularisation techniques have been developed to address this issue, which are generally complex to implement. In view of this, this paper introduces an more efficient procedure for implementation of a non-local method in Abaqus for Coupled Eulerian-Lagrangian (CEL) large deformation finite element undrained analyses. Results from a series of biaxial compression simulations demonstrate that the non-local method with a strain-softening Tresca model in CEL avoids mesh dependency. Owing to the stationary Eulerian element and the built-in mapping algorithm in CEL, high computational efficiency is achieved, adding no more than 12% to the computational cost. Guidance is provided on selection of internal length scales, element sizes and the search radius to ensure efficient non-local calculations, and it is shown that a softening scaling rule can also be used to allow use of practical mesh densities for some boundary value problems. Simulations of a number of classical geotechnical problems demonstrate the type of boundary value problems where the non-local method can effectively mitigate the mesh dependency, whilst also highlighting that the method fails to control the strain localisation that develops at soil-structure interfaces due to geometrical issues.